1. Remove and discard casings from sausages. Crumble meat into a 4- to 5-quart pan. Add onion, carrots, mushrooms, and tomato.
2. Stir often over high heat until meat begins to brown and vegetables are limp, 10 to 12 minutes.
3. Add broth and barley; scrape up browned bits. Add spinach. Bring to a boil over high heat, stirring occasionally. Cover, reduce heat, and simmer, stirring occasionally, until barley is tender to bite, about 10 minutes.
4. Ladle soup into bowls and add dollops of sour cream and salt and pepper to taste.